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arXiv · 1608.06125

Representability of Chern-Weil forms

Vamsi Pritham Pingali
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Abstract

In this paper we look at two naturally occurring situations where the following question arises. When one can find a metric so that a Chern-Weil form can be represented by a given form ? The first setting is semi-stable Hartshorne-ample vector bundles on complex surfaces where we provide evidence for a conjecture of Griffiths by producing metrics whose Chern forms are positive. The second scenario deals with a particular rank-2 bundle (related to the vortex equations) over a product of a Riemann surface and the sphere.

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Vamsi Pritham Pingali. 2016-08-22. Representability of Chern-Weil forms. https://arxiv.org/abs/1608.06125

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